Question

Please solve this I'll be glad for it​

Answer 1

Answer:

Step-by-step explanation:

Squaring on both sides

log₂ [(2x-3)/(x-1)] < 1

keeping these as powers of two

2^(log₂ [(2x-3)/(x-1)]) < 2^1

[(2x-3)/(x-1)] < 2

subracting with 2 on both sides and doing lcm

we get

1/(1-x) < 0

as 1 is positive number

So 1-x <0

there fore x > 0 -----> 1

But not only that in log there should be only +ve numbers and under should also have positive numbers by this we get

[(2x-3)/(x-1)] > 1

subtrating one on both sides and taking lcm we get

[(x-2)/(x-1)] > 0

it implies that x-2 and x-1 should have same sign

it satisfies for x<1 or x>2 ------> 2

From 1 and 2 we get

x belongs to (0,1) U (2,∞)

THANK YOU

HOPE IT IS HELPFUL

IF ANY DOUBT ASK IN COMMENT SECTION

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